- #1
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I was looking at the Wikipedia entry on the Hamilton-Jacobi equation, and was confounded by the equation at the beginning of the section on spherical coordinates:
http://en.wikipedia.org/wiki/Hamilton–Jacobi_equation#Spherical_coordinates
Shouldn't the Hamiltonian simply be
$$
H = \frac{1}{2m} \left[ p_r^2 + p_\theta^2 + p_\phi^2 \right] + U(r, \theta, \phi)
$$
?
http://en.wikipedia.org/wiki/Hamilton–Jacobi_equation#Spherical_coordinates
Shouldn't the Hamiltonian simply be
$$
H = \frac{1}{2m} \left[ p_r^2 + p_\theta^2 + p_\phi^2 \right] + U(r, \theta, \phi)
$$
?